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Warm-up 1/31/12

Warm-up 1/31/12. Given the number of sides of a regular polygon, Find: (a) the sum of the interior angles (b) one interior angle 5 sides 2. 10 sides What is the sum of the exterior angles of a 13-gon?

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Warm-up 1/31/12

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  1. Warm-up 1/31/12 • Given the number of sides of a regular polygon, • Find: (a) the sum of the interior angles • (b) one interior angle • 5 sides 2. 10 sides • What is the sum of the exterior angles of a 13-gon? • How many sides does the regular polygon have if the measure of its exterior angle is 18 degrees? (a) S= (10-2)180 = (8)(180)=1440 (a) S= (5-2)180 = (3)(180)=540 • One interior angle =1440/10 • = 144 (b) One interior angle = 540/5 = 108 360 360/18 20 sides

  2. Homework Answers: (1). No (2). Yes (3). No (4). Yes (5). No (6). Pentagon (7). Quadrilateral (8). Hexagon Convex Convex Concave (9). Hexagon (10). Dodecagon Convex Concave (11). Equilateral (12). Regular (13). Equiangular (14). Regular (15). Neither

  3. Homework Answers: (16). a. 2340 b. 360 (17). 156 24 (18). a. 3240 b. 360 (19). 162 18 (20). LMNOP pentagon (21). ABCDEF hexagon (22). 540 (23). 150 (24). x = 50

  4. 4.2 Parallelograms Essential Questions: (1). How are quadrilaterals classified by their angles or sides? (2). How are parallelograms classified? (3). How can we prove a quadrilateral is a parallelogram?

  5. Essential Question #1&2 How are quadrilaterals / parallelograms classified by their angles or sides?

  6. four four edges Quadrilaterals are polygons with ______ edges. The prefix " quad" means _________ and the word "lateral" means ________.

  7. Below are some examples and non-examples of quadrilaterals. Circle the figures you believe are quadrilaterals. A B D G C E H F

  8. A B C G D E H F Some quadrilaterals are special because they have parallel edges. If a quadrilateral has one pair of parallel edges it is called a _________. trapezoid Circle the quadrilaterals that have one pair of parallel edges.

  9. parallelogram When a figure has two pairs of parallel edges, we say that both pairs of opposite edges are parallel. A quadrilateral with both pairs of opposite edges parallel is called a ________________. Circle the quadrilaterals below that you believe are parallelograms. A C G B D H I F L E J L

  10. rhombi rhombus rectangles A and H are parallelograms that have four congruent edges. These parallelograms are called __________ (plural of __________). E, F, and H are parallelograms that have four right angles. These parallelograms are called _________. Notice that H has both four equal sides and four right angles. This parallelogram is called a _______. square

  11. Definitions: (1). Quadrilateral: (2). Parallelogram: (3). Rectangle (4). Rhombus: A polygon with exactly 4 edges. A quadrilateral with 2 pairs of opposite edges that are parallel. A quadrilateral with 4 right angles. A quadrilateral with 4 congruent edges.

  12. Definitions: (5). Square: (6). Trapezoid: A quadrilateral with 4 right angles and 4 congruent edges. A quadrilateral with exactly one pair of opposite edges that are parallel.

  13. Quadrilaterals • In the figures below, place an A in each quadrilateral, a B in each parallelogram, a C in each rectangle, a D in each rhombus, an E in each square and an F in each trapezoid.

  14. Quadrilaterals The last letter you wrote in each figure is the most specific name for that figure. Color the figures according to their most specific name. Quadrilaterals - white, Parallelograms - green, Rectangles - blue, Rhombi - orange, Squares- Yellow,Trapezoids - purple.

  15. Quadrilaterals A B A B C A A B E D C B D A B A C A B D F A B A A A F A B D

  16. Quadrilaterals A B A B C A A B E D B D A B A C A B D F A B A A A F A B D

  17. http://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpghttp://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpg . . put our heads together to…. Answer Essential Question #1 & 2 How are quadrilaterals / parallelograms classified by their angles or sides? Chart

  18. Essential Question #3 How can we prove a quadrilateral is a parallelogram?

  19. Now, we are going to find the fivespecial characteristics of all parallelograms: (1) The first characteristic is based on the definition of a parallelogram: Both pairs of opposite sides of a parallelogram are ___________. parallel

  20. The second characteristic is based on edge • lengths. Record the measure of all the angles in • the parallelograms pictured below. • If a figure is a parallelogram then both pairs of • opposite edges are _______________. 2.3 cm 3.6 cm 3.4 cm 2 cm 2 cm 1.9 cm 1.8 cm 1.8 cm 1.9 cm 3.4 cm 2.3 cm 3.6 cm congruent

  21. The third characteristic is based on angle • measures. Record the measure of all the angles • in the parallelograms below. A B 111o 69o 80o 100o 111o 69o 100o D C 80o If a figure is a parallelogram then both pairs of opposite angles are ____________. congruent

  22. (4) You will discover the fourth characteristic. Using the parallelograms above, what is special about m A and m B? ___________________ A and B are called consecutive angles. Here are some other pairs of consecutive angles: B and  C  C and  D  D and  A They are supplementary If a figure is a parallelogram then consecutive angles are ______________. (They add up to _____o). supplementary 180

  23. Now we discover the fifth and final characteristic. about a parallelogram. This characteristic pertains to the diagonals of the parallelogram. The diagonal of a polygon is a segment whose endpoints are nonconsecutive vertices of the polygon.

  24. Draw the diagonals of each parallelogram below. To do this you simply connect the points A and C with a line segment. To draw the second diagonal you connect the points B and D with a line segment. A A B A B B D D D C C C

  25. Label the point where two diagonals intersect as point X. Now, measure the lengths of the following segments: AX, XC, BX, XD. Write the length next to each segment. A A B A B B X 2.1 1.9 X 1.2 1.9 1.9 X 1.9 1.2 1.9 1.9 1.9 1.9 2.1 D D D C C C

  26. XC The segment AX is congruent to segment _____. That means that X is the _____________ of segment AC. midpoint DX The segment BX is congruent to segment _____. That means that X is the _____________ of segment BD. This conclusion leads us to the fifth characteristic of a parallelogram: midpoint The diagonals of a parallelogram _________ each other. bisect

  27. Conclusion, list the five characteristics of • all parallelograms: • 1. ___________________________________ • 2. ___________________________________ • 3. ___________________________________ • ___________________________________ • 5. ___________________________________ Opposite edges are parallel. Opposite edges are congruent. Opposite angles are congruent. Consecutive Interior Angles are Supplementary Diagonals bisect each other Remember these characteristics apply to all parallelograms, rectangles, rhombi and squares.

  28. http://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpghttp://wrir4.ucdavis.edu/PHOTOS/CROPS/images/Lettuce%20WideBeds.jpg . . put our heads together to…. Answer Essential Question #3 How can we prove a quadrilateral is a parallelogram? Chart

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